Abstract
Research presented in this paper was initiated by the publication [A. D. Agaltsov and R. G. Novikov, Examples of solving the inverse scattering problem and the equations of the Veselov–Novikov hierarchy from the scattering data of point potentials, Russian Math. Surveys 74 (2019), 3, 373–386] and is based on its results. Two sets of the complex monopole scattering coefficients are distinguished among the possible values of these coefficients for nonabsorbing inhomogeneities. These sets differ in phases of the scattering coefficients. In order to analyze the features and possibilities of reconstructing the inhomogeneities of both sets, on the one hand, the inverse problem is solved for each given value of the monopole scattering coefficient using the Novikov functional algorithm. On the other hand, the scatterer is selected in the form of a homogeneous cylinder with the monopole scattering coefficient that coincides with the given one. The results obtained for the monopole inhomogeneity and for the corresponding cylindrical scatterer are compared in the coordinate and spatial-spectral spaces. The physical reasons for the similarities and differences in these results are discussed when the amplitude of the scattering coefficient changes, as well as when passing from one set to another.
Funding source: Russian Science Foundation
Award Identifier / Grant number: 19-12-00098
Funding statement: The reported study was supported by the Russian Science Foundation, project no. 19-12-00098.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate
- A perturbation analysis based on group sparse representation with orthogonal matching pursuit
- Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition
- Space-time finite element method for determination of a source in parabolic equations from boundary observations
- On dynamical input reconstruction in a distributed second order equation
- Alternating minimization methods for strongly convex optimization
- Inverse scattering transform in two spatial dimensions for the N-wave interaction problem with a dispersive term
- Reconstruction algorithm of 3D surface in scanning electron microscopy with backscattered electron detector
- Inverse problem of Mueller polarimetry for metrological applications
- Features of solving the direct and inverse scattering problems for two sets of monopole scatterers
Artikel in diesem Heft
- Frontmatter
- Conditional stability for an inverse coefficient problem of a weakly coupled time-fractional diffusion system with half order by Carleman estimate
- A perturbation analysis based on group sparse representation with orthogonal matching pursuit
- Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition
- Space-time finite element method for determination of a source in parabolic equations from boundary observations
- On dynamical input reconstruction in a distributed second order equation
- Alternating minimization methods for strongly convex optimization
- Inverse scattering transform in two spatial dimensions for the N-wave interaction problem with a dispersive term
- Reconstruction algorithm of 3D surface in scanning electron microscopy with backscattered electron detector
- Inverse problem of Mueller polarimetry for metrological applications
- Features of solving the direct and inverse scattering problems for two sets of monopole scatterers